Is there a way to individually modify n objects with the same origin object in game engine?
The problem is that each of these objects still has the same mesh, so modifying the mesh of one object appears to modify all the meshes. Two possible solutions are: make separate meshes for each object, difficult to do in the game engine; make all the objects in blender, then load them in the game engine.
I'd suggest finding a new way to do whatever it is you're trying to do.  If this hasn't changed your mind, these two threads give some hints at what I think you're trying to do.
moving and creating objects in the game engine
creating a new mesh in the game engine